128 The Poetry of Physics and The Physics of Poetry
moving with respect to a stationary observer with the velocity v parallel
to its length. The stationary observer will discover that, in his frame
of reference, the stick has suffered a contraction and only has the length
Lo 1 −v^2 /c^2. An observer moving with the velocity, v, of the stick will
discover, however, that in his frame of reference, the stick, at rest, still
has the length Lo. In other words, as a result of its motion, an object
appears to a stationary observer to have contracted by the Fitzgerald
factor, 1 −v^2 /c^2 , which always has a value less than one but greater
than zero. The contraction of the object only takes place in the direction
parallel to its motion. The length of the object perpendicular to its motion
will appear the same to the stationary observer. A moving square will
appear, to the stationary observer, to shrink into a rectangle whose
shorter side is parallel to its motion and a moving circle will become an
ellipse with its major axis perpendicular to its motion.
When the meter stick is at rest its length will be observed to be
one meter. When the velocity of the stick is 0.5c then its length, to the
stationary observer, is observed to be 0.88 meters, as its velocity
increases to 0.88c, its length now appears to be only one-half of its
original length. When its velocity reaches 0.999c, then its length will
appear to be only 0.045 meters. As the velocity of the stick approaches
closer and closer to the velocity of light, its length appears shorter and
shorter to the stationary observer. An object traveling at the velocity of
light would literally disappear from view. This is impossible, however,
since no particles with mass can travel faster than or at the velocity of
light, as we shall soon see.
The interpretation of the Lorentz–Fitzgerald contraction within
the framework of the Theory of Relativity is quite different from the
one originally made by Lorentz and Fitzgerald. According to these
early workers, the moving meter stick actually undergoes a physical
contraction due to pressure of the aether wind arising from the absolute
motion of the meter stick with respect to the aether. The contraction is
due to the absolute motion of the meter stick. From their point of view, if
the observer were to move and the meter stick remained stationary, the
observed would not observe a contraction. In the Theory of Relativity, on
the other hand, the contraction is observed whether the stick moves with
respect to the observer or the observer moves with respect to the stick.
Furthermore, the stick does not actually physically contract. An observer
moving with the stick does not observe a change in its length. The stick
appears shorter to the stationary observer because his concept of space is